Some properties of the Gumbel-Weibull distribution including the mean deviations and modes are studied. A detailed discussion of regions of unimodality and bimodality is given. The method of maximum likelihood is proposed for estimating the distribution parameters and a simulation is conducted to study the performance of the method. Three tests are given for testing the significance of a distribution parameter. The applications of GumbelWeibull distribution are emphasized. Five data sets are used to illustrate the flexibility of the distribution in fitting unimodal and bimodal data sets.

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The article argues that the persistence of student difficulties in reasoning about the stochastic, despite significant reform efforts, might be the result of the continuing impact of the formalist mathematical tradition, affecting instructional approaches and curricula and acting as a barrier to instruction that provides students with the skills necessary to recognize uncertainty and variability in the real world. It describes a study driven by the conjecture that the reform movement would have been more successful in achieving its objectives if it were to put more emphasis on helping students build sound intuitions about variation. It provides an overview of how the conjecture guiding the study was developed and linked to classroom practice, and briefly discusses the experiences and insights gained from a teaching experiment in a college level, introductory statistics classroom, which adopted a nontraditional approach to statistics instruction with variation at its core. By contrasting students’ intuitions about the stochastic prior to instruction to their stochastical reasoning at the completion of the course, it illustrates the potential of the instructional approach as an alternative to more conventional instruction. First published December 2002 at Statistics Education Research Journal: Archives

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Engineers utilize screening experiments to find significant main effects of factors for quality improvement. After the analysis of the data resulting from this type of experiment, further investigation into the significance of some two-factor interactions might be desirable. Repeating an experiment of the same size can be costly and time consuming. A follow-up experiment with half the number of runs from the initial experiment is a good alternative. In this article, we propose two strategies for selecting additional runs to investigate the significance of two-way interactions that are important to the experimenter. These strategies are based on the findings from the initial experiment. Two examples are presented to illustrate the application of these strategies.